Does the Canon EOS-1D X Ethernet support DHCP, and why is transfer speed below 1Gbps?

Basically this question conflates the carrying capacity of gigabit Ethernet with the overall system performance, which is why you aren't seeing the results you expected. The problem is not so much a case of being unresolved, but that the expectations were unrealistic.

The actual throughput will be limited by the slowest of all the various data pathways that the data has to travel.

By the looks of how Canon have implemented it as a server service on the camera, the image will most likely be written to flash and read back to be sent over the network. That limits the fastest speed you can put over the network to the rate you can write AND read a file - so lets simplistically assume UDMA7 (167MB/s) and that read and write are both the same (actually they aren't). Your max is around 80MB/s x8 (so 640Mb/s) maximum in a perfect world.

You have a low-power ARM CPU processor which will be busy doing its own thing like making sure the images hit the flash as quickly as possible, controlling the display, responding to user input and controlling what the DIGIC processors are doing. There are a whole bunch of other things that will be more important to it than ferrying data from flash to the network.

Then once you get out of the camera, assuming the network is otherwise idle you have to contend with the overheads of Ethernet and of using TCP/IP on top of it (around 2 to 8%.) If they're using HTTP then there will be a lot of additional communication overhead on top and a need for data to be sent, checked for errors and acknowledged before another chunk of data is sent. That's if the system receiving the data can handle getting data that quickly which is not a given.

It's not an exhaustive list but it should give you a good idea of what has to go on to get an image from camera to desktop.